If every email that aims at making you react in some way is spam, then every email is spam. What communication is not meant to influence the recipient? Spam, probably.
In an interesting twist, I think spam can be defined as the inverted duplicate of what we started with. Spam is
- unsolicited email that is not intended by the sender to make the recipient react in a certain manner.
I don't think this definition is perfect. Quite to the contrary. I'm eager to hear what you think, discuss, and improve on this beginning.